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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19521030 |
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Table of Contents:
- <p>Phase Calculus is presented in its current stack as a single lifted-object formalism rather than as a loose collection of phase pictures, arithmetic tricks, or downstream branch-specific rules. The native state is the carried lifted object</p> <p><code>Xi = (b, A, q, theta, kappa, c), q = (u, v), c = <theta - pi<em>u</em>v, theta + pi<em>u</em>v></code></p> <p>evolved by one parent grammar and then read through branch-specific projectors. This demonstration paper does not re-prove the long merged formalisation. Its purpose is narrower: to show, in one readable document, how the same lifted object supports the operator core of Phase Calculus, the selector-closed executable macro-calculus, the completion/shadow branch, the quotient-descent interface to the physics stack, and the four-filter hierarchy including the biological readout. The paper has three central results.</p> <ul> <li>First, it restates the single spine of the formalism: primitive roll, lifted state, operator alphabet <code>{Q, B, L}</code>, selector-closed macro-calculus<code> {R, S, T}</code>, exact quotient criterion, and arithmetic-completion bridge to the canonical anchor (55, 89) with carried coefficients 1/24 per edge and 1/12 two-sided.</li> <li>Second, it records the computational evidence from the four-filter package: green, blue, red, and yellow are faithful covariant readouts of the same lifted state under the same operator grammar, with exact-zero primary gate errors, machine-precision recovery errors, and sharp negative controls when the state is stripped to product-only or loses its sheet index. </li> <li>Third, it shows how the yellow filter closes two descents at once: the CF01 quantum-geometric-tensor bridge and a native biological scaffold. In this v2 paper the biological count structure is not imported. From the quarter alphabet generated by Q, the three-slot selector block, and the normalized edge residual 24*E_edge = 1, the paper derives internally the weight budget (1, 2, 1, 1), the total scaffold size 240, the base-centered counts (56, 72, 56, 56), and the host-indexed bifurcations 240 = (128, 112) -> ((72, 56),(56, 56)). The unification claim is therefore precise and limited. One singular lifted object is taken as the native source of the current</li> </ul> <p>Phase Calculus hierarchy and of the physics branches that descend from it by quotient projection, while also admitting a biological projection whose scaffold counts are now derived internally and only then compared with the external codon:anticodon / E8 report. The closing section states explicitly what is closed, what remains imported, and what is still not unique.</p>